>
> Probably you should use shortestPath() 
> <http://www.orientechnologies.com/docs/last/SQL-Functions.html#shortestpath> 
> function 
> if there are only two vertices, and your LCA is the vertex where edge 
> direction changes.

If there are few vertices, you can make few shortestPath() queries passing 
in, at first, any two vertices, than returned LCA of those 2 and any vertex 
of the rest. When all vertices come to end, the returned LCA is yours. 
Also you can write some Java code for this functionality. 
 

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